**Complex Voltage and Current**

In order to simplify calculations, sinusoidal voltage and current waves are commonly represented as complex-valued functions of time denoted as and .

Impedance is defined as the ratio of these quantities.

Substituting these into Ohm's law we have

Noting that this must hold for all, we may equate the magnitudes and phases to obtain

The magnitude equation is the familiar Ohm's law applied to the voltage and current amplitudes, while the second equation defines the phase relationship.

Read more about this topic: Electrical Impedance

### Other articles related to "complex voltage and current, complex, voltage, current":

**Complex Voltage and Current**- Phasors

... A phasor is a constant

**complex**number, usually expressed in exponential form, representing the

**complex**amplitude (magnitude and phase) of a sinusoidal function of time ... can be defined as the ratio of the phasor

**voltage**across the element to the phasor

**current**through the element, as determined by the relative amplitudes and phases of ...

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